Method for Forming Circular Patterns on a Surface

ABSTRACT

A method for forming patterns on a surface using charged particle beam lithography is disclosed, in which a stencil is provided comprising first and second apertures, where circular or nearly-circular patterns in a first plurality of sizes are formed on the surface using the first aperture by varying shot dosage, and where circular or nearly-circular patterns in a second plurality of sizes are formed on the surface using the second aperture by varying shot dosage. A similar method for fracturing or mask data preparation is also disclosed. A stencil for charged particle beam lithography is also disclosed, where the stencil comprises first aperture and second apertures capable of forming, in one shot, patterns in a first and a second range of sizes on a surface by varying the shot dosage, where the first range of sizes is discontinuous with the second range of sizes.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/723,181 filed on Dec. 20, 2012, entitled “Method For Forming CircularPatterns On A Surface” and published as U.S. Patent ApplicationPublication No. 2013-0122405, which is hereby incorporated by reference.U.S. patent application Ser. No. 13/723,181 is a continuation of U.S.patent application Ser. No. 13/282,446 filed on Oct. 26, 2011 entitled“Method, Device, And System For Forming Circular Patterns On A Surface”,which is a continuation of U.S. patent application Ser. No. 12/540,322filed on Aug. 12, 2009 entitled “Method and System For Forming CircularPatterns On a Surface” and issued as U.S. Pat. No. 8,057,970, both ofwhich are hereby incorporated by reference for all purposes. U.S. patentapplication Ser. No. 12/540,322: 1) is a continuation-in-part of U.S.patent application Ser. No. 12/202,364 filed Sep. 1, 2008, entitled“Method and System For Manufacturing a Reticle Using CharacterProjection Particle Beam Lithography” and issued as U.S. Pat. No.7,759,026; 2) is a continuation-in-part of U.S. patent application Ser.No. 12/473,241 filed May 27, 2009, entitled “Method for Manufacturing aSurface and Integrated Circuit Using Variable Shaped Beam Lithography”and issued as U.S. Pat. No. 7,754,401; 3) claims priority from U.S.Provisional Patent Application Ser. No. 61/224,849 filed Jul. 10, 2009,entitled “Method and System for Manufacturing Circular Patterns On aSurface And Integrated Circuit”; and 4) is related to U.S. patentapplication Ser. No. 12/540,321 filed Aug. 12, 2009, entitled “MethodFor Fracturing Circular Patterns and For Manufacturing a SemiconductorDevice” and issued as U.S. Pat. No. 8,017,288; all of which are herebyincorporated by reference for all purposes.

BACKGROUND OF THE DISCLOSURE

The present disclosure is related to lithography, and more particularlyto the design and manufacture of a surface which may be a reticle, awafer, or any other surface, using charged particle beam lithography.

In the production or manufacturing of semiconductor devices, such asintegrated circuits, optical lithography may be used to fabricate thesemiconductor devices. Optical lithography is a printing process inwhich a lithographic mask or photomask manufactured from a reticle isused to transfer patterns to a substrate such as a semiconductor orsilicon wafer to create the integrated circuit. Other substrates couldinclude flat panel displays or even other reticles. Also, extremeultraviolet (EUV) or X-ray lithography are considered types of opticallithography. The reticle or multiple reticles may contain a circuitpattern corresponding to an individual layer of the integrated circuitand this pattern can be imaged onto a certain area on the substrate thathas been coated with a layer of radiation-sensitive material known asphotoresist or resist. Once the patterned layer is transferred the layermay undergo various other processes such as etching, ion-implantation(doping), metallization, oxidation, and polishing. These processes areemployed to finish an individual layer in the substrate. If severallayers are required, then the whole process or variations thereof willbe repeated for each new layer. Eventually, a combination of multiplesof devices or integrated circuits will be present on the substrate.These integrated circuits may then be separated from one another bydicing or sawing and then may be mounted into individual packages. Inthe more general case, the patterns on the substrate may be used todefine artifacts such as display pixels or magnetic recording heads.

In the production or manufacturing of semiconductor devices, such asintegrated circuits, maskless direct write may also be used to fabricatethe semiconductor devices. Maskless direct write is a printing processin which charged particle beam lithography is used to transfer patternsto a substrate such as a semiconductor or silicon wafer to create theintegrated circuit. Other substrates could include flat panel displays,imprint masks for nano-imprinting, or even reticles. Desired patterns ofa layer are written directly on the surface, which in this case is alsothe substrate. Once the patterned layer is transferred the layer mayundergo various other processes such as etching, ion-implantation(doping), metallization, oxidation, and polishing. These processes areemployed to finish an individual layer in the substrate. If severallayers are required, then the whole process or variations thereof willbe repeated for each new layer. Some of the layers may be written usingoptical lithography while others may be written using maskless directwrite to fabricate the same substrate. Eventually, a combination ofmultiples of devices or integrated circuits will be present on thesubstrate. These integrated circuits are then separated from one anotherby dicing or sawing and then mounted into individual packages. In themore general case, the patterns on the surface may be used to defineartifacts such as display pixels or magnetic recording heads.

In semiconductor manufacturing, reliably manufacturing contacts and viasis difficult and important, especially when optical lithography is usedto manufacture patterns smaller than 80 nm half pitch, where half pitchis one-half of the minimum contact or via size plus one-half of theminimum required space between contacts or vias. Contacts and viasconnect a conductive material on one layer to another conductivematerial on another layer. In older technology nodes which wererelatively larger than currently-popular technology nodes, attempts weremade to manufacture square vias and contacts on the wafer. Squarecontacts and vias are desirable so as to maximize the amount of areathat connects between the conductive material in the below layer and theconductive material in the above layer. But with decreasing featuresizes, it has become prohibitively expensive or impractical to createlarge numbers of square patterns on the semiconductor wafer. Especiallyat 80 nm half pitch and below, semiconductor manufacturers targetforming near-circles on the wafer, when viewed from above, which createnearly cylindrical contacts or vias. The design data that specifies thedesired wafer shape still specifies the desired shape as a square.However, the manufacturers and designers alike work with the assumptionthat limitations of the optical lithographic process will cause theactual resulting shape to be a near-circle on the wafer. The generalizedcase of this effect for all shapes is sometimes referred to as cornerrounding.

A significant advantage to the conventional practice of specifyingcontacts and vias as squares in the design data is that square patternscan be formed relatively quickly on a reticle. The use of squarepatterns for contacts and vias on the reticle and photomask, however,make the manufacturing of vias and contacts on the semiconductor devicemore difficult. It would be advantageous to eliminate the manufacturingdifficulties associated with using square patterns on a photomask forcontacts and vias, particularly for half-pitches less than 80 nm.

SUMMARY OF THE DISCLOSURE

A method for forming patterns on a surface using charged particle beamlithography is disclosed, in which a stencil is provided comprising afirst aperture and a second aperture, where circular or nearly-circularpatterns in a first plurality of sizes are formed on the surface usingthe first aperture by varying shot dosage before proximity effectcorrection (PEC), and where circular or nearly-circular patterns in asecond plurality of sizes are formed on the surface using the secondaperture by varying shot dosage before PEC.

A method for fracturing or mask data preparation for charged particlebeam lithography is also disclosed, in which a set of shots isdetermined which will form a set of circular or nearly-circular patternson a surface, where the set of circular or nearly-circular patternscomprises patterns in a plurality of sizes, where a first shot uses afirst character projection (CP) character, and where a second shot usesa second CP character, where the first CP character is smaller than thesecond CP character.

A stencil for charged particle beam lithography is also disclosed, wherethe stencil comprises a first aperture capable of forming, in one shot,patterns in a first range of sizes on a surface by varying the shotdosage, and where the stencil comprises a second aperture capable offorming, in one shot, patterns in a second range of sizes on a surfaceby varying the shot dosage, where the first range of sizes isdiscontinuous with the second range of sizes.

These and other advantages of the present disclosure will becomeapparent after considering the following detailed specification inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a conventional method of forming circular patternssuch as contacts or vias on a wafer;

FIG. 2 illustrates a method of forming circular patterns such ascontacts or vias on a wafer by the current disclosure;

FIG. 3 illustrates a charged particle beam writer with characterprojection (CP) capability;

FIG. 4 illustrates a character projection stencil containing a pluralityof circular characters;

FIG. 5A illustrates a pattern formed by a shot of a circular characterprojection character;

FIG. 5B illustrates the effect of varying dosage on the size of thepattern on the surface registered by the character projection shot ofFIG. 5A;

FIG. 6 illustrates a chart showing the range of diameters of circularpatterns than can be formed on a surface using a set of circularcharacter projection characters;

FIG. 7 illustrates how overlapping VSB shots may be used to write acircular pattern;

FIG. 8 illustrates how non-overlapping VSB shots may be used to write acircular pattern;

FIG. 9 illustrates a circular pattern that can be created on a surfaceusing a parameterized glyph;

FIG. 10 illustrates a conceptual flow diagram of manufacturing a reticleand fabricating an integrated circuit using an exemplary method of thecurrent disclosure;

FIG. 11A illustrates a desired near-circular pattern; and

FIG. 11B illustrates a set of non-overlapping VSB shots that can formthe pattern of FIG. 11A.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 illustrates the conventional practice for forming contact and viapatterns on a wafer using optical lithography. An optical lithographymachine 100 comprises an illumination source 102 which emits opticalradiation onto a photomask 104 containing a multiplicity of rectangularaperture patterns 106. Optical radiation is transmitted through theaperture pattern 106 and through one or more lenses 108, thereby forminga pattern 110 on a surface 112, such as a semiconductor wafer. Thepattern 110 on the surface 112 is generally reduced in size compared tothe aperture pattern 106 on the photomask 104. Due to limitations of theoptical lithography process, such as the wavelength of the radiationcreated by the illumination source 102, for small contact and viapatterns, such as for patterns smaller than 80 nm half pitch, the squarepattern on the photomask causes a circular or near-circular pattern tobe formed on the substrate.

There is an important concept called Mask Error Enhancement Factor(MEEF) in semiconductor lithography. In a typical semiconductormanufacturing process using photomasks, the photomasks are four timesthe dimensions of the wafer. For example, a 50 nm target shape on asurface appears as a 200 nm shape on the photomask. If MEEF was 1.0, a 4nm offset error on the photomask would translate to a 1 nm offset on thewafer. However, a typical MEEF for lines and spaces, such as oninterconnect or wiring layers, is 2. For contact layers, a typical MEEFis 4, which means that a 4 nm offset error on the photomask translatesto a 4 nm offset on the wafer. In advanced technology nodes withcontacts layers which are less than 80 nm half-pitch, a MEEF as high as10 may be projected. In such a case a 4 nm offset on the photomasktranslates into a 10 nm offset on the wafer. Thus photomasks, andparticularly photomasks for contact layers, are required to be extremelyaccurate in order that the MEEF-multiplied error on the surface does notexceed the maximum-allowed error.

One known method for improving MEEF is the so-called perimeter rule. Theperimeter rule states that for a given enclosed shape, a higher ratio ofthe shape's perimeter to the shape's area results in a larger MEEF. Insemiconductor manufacturing, it is most important in the lithographystep to expose the resist with the right amount of total energy for eachshape on the mask. Therefore, for each pattern or shape, accuracy ismore important for the total area than the other dimensions of thepattern or shape. Various sources of error in the semiconductormanufacturing processes act on the perimeter, which are the set of edgesthat enclose the shape. These edges may move inward or outward comparedto the desired location. When the ratio of the perimeter to the area isrelatively large, the entire perimeter moving inwards by a givendistance, say 1 nm, shrinks the enclosed area by a larger amount than ifthe ratio was relatively smaller. Because total area is total energy,and the total energy is critical for each shape, a smaller ratio isdesired for every shape. Among geometric shapes, a circle has thesmallest perimeter per unit area of any shape. Therefore, circularshapes or patterns will have a smaller MEEF than any non-circular shape.Nearly-circular shapes will have a MEEF that is almost optimal.

FIG. 2 illustrates how contacts or vias can be created on the siliconwafer by the current disclosure. An optical lithography machine 200comprises an illumination source 202 which emits optical radiation ontoa photomask 204 containing a multiplicity of circular aperture patterns206. Optical radiation is transmitted through the aperture pattern 206and through one or more lenses 208, thereby forming a pattern 210 on asurface 212, such as a semiconductor wafer. Because of theabove-mentioned perimeter rule, use of the circular or near-circularaperture 206 on the photomask 204 results in a lower (better) MEEF thanuse of the square aperture 106 on the photomask 104 of FIG. 1.

Mask making today is done by either a laser-based mask writer, or acharged particle beam mask writer, such as an electron beam mask writer.Today's production tools for the most advanced technology nodes with thesmallest features below 80 nm half pitch are all done using an electronbeam mask writer using variable shaped beam (VSB) technology with a highvoltage (50 KeV and above) electron gun. Conventional reticle or maskwriting includes a step of fracturing all desired mask shapes intoconstituent rectangles and 45 degree triangles of a certain size limit(for example, between 1 nm wide and 1000 nm wide) such that the union ofall shapes is the original shape, perhaps within a certain minimumthreshold, and such that the constituent shapes do not overlap. Thefractured shapes are individually written by the electron beam maskwriter as VSB shots. Reticle writing typically involves multiple passeswhereby the given shape on the reticle is written and overwritten.Typically, two to four passes are used to write a reticle to average outerrors, allowing the creation of more accurate photomasks.Conventionally, within a single pass the constituent shapes do notoverlap. In reality, because electron beam mask writers are notperfectly accurate, some VSB shots that were designed to abut willoverlap slightly. Also, between some VSB shots that were designed toabut there will be minute gaps. The electron beam mask writer'splacement accuracy and the semiconductor design are carefullycoordinated to avoid problems that arise due to these overlaps and gaps.The problems that arise are minimal particularly for small errors of 1nm or below because the electron beam being transmitted has a naturalblurring radius (roughly of 20-30 nm size), causing a Gaussiandistribution of transferred energy beyond the drawn edges of the shapes.The dose for each of the VSB shots is assigned in a later and separatestep. The dose determines the shutter speed, or the amount of time thatthe electrons are being transmitted to the surface. Proximity EffectCorrection and other corrective measures determine what doses should beapplied to each VSB shot to make the resulting photomask shape as closeto the originally-desired photomask shape as possible.

Conventionally, one VSB shot is required for forming a square contact orvia pattern. Forming a circular pattern on a reticle using conventionalmask writing technology requires many VSB shots. Increasing the numberof VSB shots has a direct impact on the amount of time required to writethe reticle, which directly translates to photomask cost. Since for atypical integrated circuit design, many million contact and via patternsmust be formed, the formation of circular contact or via patterns on areticle using conventional VSB shots is not considered practical.

FIG. 7 illustrates an example of how a small circular pattern 700 may beformed on a surface such as a reticle by the current disclosure usingmultiple overlapping VSB shots. In the FIG. 7 example three VSBshots—rectangular shot 702, rectangular shot 704 and square shot 706—areshown. Use of overlapping shots allows the pattern to be written withfewer VSB shots than would be required with conventional methods. Thetechnique of overlapping shots is particularly effective for smallcircles where the blur of the charged particle beam caused by forwardscattering of the charged particles, Coulomb effect, and other physical,chemical, and electromagnetic effects is of the same order of magnitudeas the diameter of the circle. As can be seen in FIG. 7, the union ofthe three VSB shots, shot 702, shot 704 and shot 706, does not equal thetarget circular pattern 700. The dosage of each shot is shown as afraction of the “normal” VSB dose: shot 702 and shot 704 have dosages of0.7 times normal, and shot 706 has a dosage of 0.6 times normal. Asshown, the total dosage summed from all shots in the middle 710 of thecircle 700 is therefore 2.0 times normal. Some mask fabricationprocesses have a maximum dosage limit, such as 2.0 or twice the normaldosage. To compensate for the lower-than-normal shot dosages, the VSBshot boundaries for shots 702, 704, and 706 are extended beyond theboundary of the target circle 700. Charged particle beam simulation maybe used to calculate the pattern that will be formed on the surface, soas to verify that the resultant pattern is within a desired tolerance ofthe target circular pattern 700.

FIG. 8 illustrates an example of how a small circular pattern 802 may beformed on a surface such as a reticle by the current disclosure usingmultiple non-overlapping VSB shots. In this example, five shots areused: shot 804, shot 806, shot 808, shot 810 and shot 812. As can beseen, the union of the shots 804, 806, 808, 810 and 812 is differentthan the target pattern 802. The use of five shots to fill the patternstill represents a reduced shot count compared to conventional methods,in which shots are generated to match the boundary of the targetcircular pattern as closely as possible. In the FIG. 8 example the shotboundaries do not extend as far beyond the boundary of the targetcircular pattern as in the FIG. 7 example because the dosages of theFIG. 8 individual VSB shots can be made higher than the dosages of theFIG. 7 VSB shots without concern of exceeding a maximum dosage limit,since the VSB shots in the FIG. 8 example do not overlap. As with theexample of FIG. 7, charged particle beam simulation may be used tocalculate the pattern that will be formed on the surface, so as toverify that the resultant pattern is within the desired tolerance of thetarget circular pattern 802.

FIG. 3 illustrates a charged particle beam writer 300 which hascharacter projection (CP) capability. As shown, a particle or electronbeam source 302 provides a particle or electron beam 304 to a first mask308 that can be formed to a rectangular shape 310 with a first aperture306 formed in the first mask 308. The rectangular beam 310 is thendirected to a second mask or stencil 312 and through a second apertureor character 314 formed in the stencil 312. The portion of the chargedparticle beam 310 that goes through character 314 is directed to surface326, where it forms a pattern 324 in the shape of character 314. In thisexemplary embodiment of FIG. 3, the stencil 312 also includes threecircular characters of various sizes: character 316, character 318 andcharacter 320. The stencil 312 also includes a rectangular aperture 322for VSB shots, allowing the creation of VSB and CP shots using the samestencil 312. Currently-available CP charged particle beam systems can beused for forming patterns directly onto substrates such as siliconwafers, but are not suitable for writing reticles for creation ofphotomasks. Even if character projection (CP) capability was availableon charged particle beam writers for reticles, the conventional maskwriting methodology and systems would only be able to writepre-designated diameters of circles, based on the sizes of circular CPcharacters on the stencil, such as character 316, character 318 andcharacter 320 on stencil 312. Using the conventional methodology, thenumber of alternative sizes would be limited by the number of charactersthat could be placed on a stencil.

FIGS. 5A&B illustrate an example of how a single CP character may beused to form circles of varying diameters on a surface, by varying theshot dosage. FIG. 5A shows a nominal circular pattern 500 that can beformed on a surface using a CP charged particle beam writer such as thatshown in FIG. 3 using a circular CP character such as character 318. Aline 502 bisects the circular pattern 500. FIG. 5B shows the dosagedistribution along the line 502 through pattern 500. The horizontal axiscorresponds to the linear position along line 502, and the vertical axisshows the dosage. Three dosage distributions are shown: for shot dosage504, shot dosage 506 and shot dosage 508. Each of the dosage curvesillustrates the Gaussian distribution of the charged particle beam. FIG.5B also shows a resist threshold level 520, which is the dosage levelabove which a pattern will be registered on the surface. As shown, thegreatest shot dosage 504 will register a pattern of size 510, theintermediate shot dosage 506 will register a pattern of medium size 512,and the lowest shot dosage 508 will register a pattern of smallest size514. Since the pattern is circular, this size difference is a diameterdifference. Thus, different diameter circles can be formed on thesurface using a single CP character by varying the shot dosage.

FIG. 4 illustrates an exemplary embodiment of a CP stencil containing aplurality of circular CP characters of varying sizes. Stencil 402contains five circular CP characters of different sizes: character 404,character 406, character 408, character 410 and character 412.Additionally, stencil 402 contains a rectangular aperture 414 for VSBshots and a set of triangular apertures 416, also for VSB shots. In someembodiments of the present invention stencil 402 may not containtriangular apertures 416, but may contain only rectangular and circularapertures. Each circular CP character 404, 406, 408, 410, and 412 canform circular patterns in a range of diameters on a surface, by varyingthe shot dosage as described above. By appropriately choosing the sizesof the circular CP characters during the design of the stencil, circularpatterns in a wide range of sizes can be formed on a surface. FIG. 6illustrates a chart showing an example of how a group of five circularCP characters of appropriate sizes may be used to form circles in alarge range of sizes on a surface. In the example of FIG. 6, CPcharacter “A” can form circular patterns in a range of sizes 602. CPcharacter “B” can form circular patterns in a range of sizes 604. CPcharacter “C” can form circular patterns in a range of sizes 606. CPcharacter “D” can form circular patterns in a range of sizes 608. CPcharacter “E” can form circular patterns in a range of sizes 610. Asshown, the range of sizes 602 overlaps the range of sizes 604, the rangeof sizes 604 overlaps the range of sizes 606, the range of sizes 606overlaps the range of sizes 608, and the range of sizes 608 overlaps therange of sizes 610. Therefore, a circular pattern of any size in thetotal range 620 can be formed using only five CP characters. It is notstrictly necessary that the range of diameters overlap to anysignificant degree, but only that the largest circle that can be formedwith one circular CP character is at least as large as the smallestcircle that can be formed using the next-larger circular CP character.In other embodiments, it is not necessary that the range of possiblediameters be continuous. The available sizes of circular patterns whichcan be formed using characters on the stencil 402 may be a plurality ofdiscontinuous ranges of sizes.

Two-dimensional maps of dosages known to be generated on a surface bysingle charged particle beam shots or combinations of charged particlebeam shots are called glyphs. Each glyph may have associated with it theposition and shot dosage information for each of the charged particlebeam shots comprising the glyph. A library of glyphs may be pre-computedand made available to fracturing or mask data preparation functions.Glyphs may also be parameterized. FIG. 9 illustrates an example of acircular pattern on a surface which represents a set of patterns thatcan be formed by a parameterized glyph. The parameter of the glyph 902is its diameter “d”, where “d” may be any value between 50 and 100units. In one embodiment, the glyph may be calculated using a set ofcircular CP characters which, using variable shot dosage, can generateany dosage map representing circular patterns within the size range of50 to 100 units.

It should be noted that, as is common in integrated circuit design, atwo-dimensional shape, such as a circle, refers to a shape on thesemiconductor wafer as viewed from top-down. In the case of contacts andvias, the actual three-dimensional manufactured shapes may becylindrical or nearly cylindrical.

The methods set forth herein for forming circles on surfaces such asreticles using either VSB shots or circular CP characters may also beused to form patterns directly on substrates such as silicon wafers,using maskless direct write. It should be noted that MEEF is not anissue for direct writing.

The techniques of the present disclosure may also be used when thedesired pattern to be formed on a surface is nearly-circular. FIG. 11Aillustrates a nearly-circular pattern 1102 that may be a desired maskpattern for a contact or via. The pattern 1102 may, for example, be adesirable trade-off between MEEF and maximal contact area between theconductive material in the layer above the contact or via and theconductive material in the layer below the contact or via. FIG. 11Billustrates a five-shot group 1104 of VSB shots, in this examplenon-overlapping VSB shots, that can, with proper dosages, register apattern on the surface which is close to the desired pattern 1102. Shotgroup 1104 consists of shot 1110, shot 1112, shot 1114, shot 1116 andshot 1118, which in this exemplary embodiment are rectangular shots ofdiffering widths and heights. Dosages of the shots in shot group 1104may vary with respect to each other. The pattern registered on resistcoating the surface is shape 1120, which is equivalent to shape 1102,within a pre-determined tolerance. The example illustrates hownearly-circular patterns can be formed with the techniques of thisdisclosure.

The formation of circles on a surface can be approximated by anon-circular shape such as a polygon. Where a circle is desired on asurface or on a substrate such as a silicon wafer, the result may be anear-circle, such as a curvilinear shape which closely resembles acircle.

FIG. 10 is a conceptual flow diagram 1000 of an embodiment of thepresent disclosure for preparing a surface for use in fabricating asubstrate such as an integrated circuit on a silicon wafer using opticallithography. The input for this process is a set of desired patterns1002 to be formed on a photomask. The set of desired patterns 1002 mayinclude a set of desired circular patterns, which are received by aninput device. Step 1004 is a mask data preparation (MDP) step. MDP step1004 may include a fracturing operation in which shot overlap may or maynot be allowed, and in which other-than-normal dosage assignment isallowed. The fracturing may comprise determining a set of VSB shots, ormay comprise determining a CP character and shot dosage, using the CPstencil information 1006, or may comprise determining a combination ofVSB and CP shots. MDP step 1004 may also comprise selecting one or moreglyphs from a glyph library 1008 to match a desired pattern. Theselected glyphs may include parameterized glyphs. MDP step 1004 may alsoinclude an operation of determining the optimal method—VSB shots, a CPcharacter shot, or a glyph—to use for each desired pattern. Theoptimization criteria may, for example, be to minimize shot count orcharged particle beam system writing time. MDP step 1004 may alsocomprise using particle beam simulation to calculate the pattern thatwill be formed on the surface by a set of shots, and may also compriserevising the set of shots and recalculating the pattern if thecalculated pattern differs from the desired pattern by more than apredetermined tolerance. Particle beam simulation may include any offorward scattering, resist diffusion, Coulomb effect, backwardscattering, loading, fogging, and etching simulation, and may usecharged particle beam system and process information 1010. MDP step 1004outputs to an output device a determined shot list 1012 comprising thecombined list of VSB and CP shots, and shots from glyphs. The shots inthe shot list 1012 contain dosage information. In step 1014 proximityeffect correction (PEC) and/or other corrections may be performed orcorrections may be refined from earlier estimates. Step 1014 uses shotlist 1012 as input and produces a final shot list 1016 in which the shotdosages have been adjusted. The final shot list 1016 is used by thecharged particle beam system 1018 to expose resist with which thereticle has been coated, thereby forming a set of patterns 1020 on theresist. After various processing steps 1022, the reticle is transformedinto a photomask 1024. The photomask 1024 is used in an opticallithography machine 1026 to transfer the set of desired patterns, suchas circular patterns, on the photomask 1024 onto a substrate such as asilicon wafer, creating a wafer image 1028, from which the silicon waferis produced.

A glyph creation step 1030 in FIG. 10 calculates dosage maps either froma CP character shot with a particular dosage or from a set of VSB shotshaving possibly various dosages. Glyph creation step 1030 uses CPstencil information 1006. The CP stencil information may includeinformation about a plurality of differently-sized circular CPcharacters. Glyph creation step 1030 may also comprise using chargedparticle beam simulation to calculate the glyph. Particle beamsimulation of the glyph may include any of forward scattering, resistdiffusion, Coulomb effect, and etching simulation, and may use chargedparticle beam system and process information 1010. Glyph creation step1030 may also comprise calculation of a set of glyphs to create aparameterized glyph.

The various flows described in this disclosure may be implemented usinggeneral-purpose computers with appropriate computer software ascomputation devices. Due to the large amount of calculations required,multiple computers or processor cores may also be used in parallel. Inone embodiment, the computations may be subdivided into a plurality of2-dimensional geometric regions for one or more computation-intensivesteps in the flow, to support parallel processing. In anotherembodiment, a special-purpose hardware device, either used singly or inmultiples, may be used to perform the computations of one or more stepswith greater speed than using general-purpose computers or processorcores. The optimization and simulation processes described in thisdisclosure may include an iterative optimization process such as withsimulated annealing, or may constitute solely a constructive, greedy,deterministic or other process without iterative improvement.

All references in this disclosure to circles should be interpreted toalso include near-circles. Similarly, all references to circularpatterns, circular apertures, circular characters, or circular CPcharacters should be interpreted to also include nearly-circularpatterns, apertures, characters, or CP characters. Also, all referencesto cylinder should be interpreted to include near-cylinder, and allreferences to cylindrical should include nearly-cylindrical.

While the specification has been described in detail with respect tospecific embodiments, it will be appreciated that those skilled in theart, upon attaining an understanding of the foregoing, may readilyconceive of alterations to, variations of, and equivalents to theseembodiments. These and other modifications and variations to the presentsystem and method for manufacturing circular patterns on a surface ormethod for manufacturing an integrated circuit or method and system forfracturing or mask data preparation may be practiced by those ofordinary skill in the art, without departing from the spirit and scopeof the present subject matter, which is more particularly set forth inthe appended claims. Furthermore, those of ordinary skill in the artwill appreciate that the foregoing description is by way of exampleonly, and is not intended to be limiting. Thus, it is intended that thepresent subject matter covers such modifications and variations as comewithin the scope of the appended claims and their equivalents.

1-35. (canceled)
 36. A method for forming patterns on a surface usingcharged particle beam lithography, the method comprising: providing astencil comprising a first aperture and a second aperture, wherein afirst size of the first aperture is different than a second size of thesecond aperture; forming circular or nearly circular patterns on thesurface in a first plurality of sizes using the first aperture, whereinthe patterns are formed in the first plurality of sizes by varying shotdosage before proximity effect correction (PEC), and wherein the firstplurality of sizes comprises a first range; and forming circular ornearly circular patterns on the surface in a second plurality of sizesusing the second aperture, wherein the patterns are formed in the secondplurality of sizes by varying the shot dosage before PEC, and whereinthe second plurality of sizes comprises a second range.
 37. The methodof claim 36 wherein the first range and the second range arediscontinuous.
 38. A method for fracturing or mask data preparation forcharged particle beam lithography, the method comprising: determining aset of shots that forms a set of circular or nearly circular patterns ona surface, wherein the set of circular or nearly circular patternscomprises patterns in a plurality of sizes, and wherein the set of shotscomprises: a first shot using a first circular or nearly-circularcharacter projection (CP) character; and a second shot using a secondcircular or nearly-circular CP character, wherein the first CP characteris smaller than the second CP character, and wherein the determining isperformed using one or more computing hardware processors.
 39. Themethod of claim 38 wherein a first range of sizes of patterns that canbe formed using the first CP character does not overlap a second rangeof sizes of patterns that can be formed using the second CP character.40. The method of claim 38 wherein the determining comprises calculatingsizes of the circular or nearly-circular patterns on the surface. 41.The method of claim 40 wherein the calculating comprises chargedparticle beam simulation.
 42. The method of claim 41 wherein the chargedparticle beam simulation includes at least one of a group consisting offorward scattering, resist diffusion, Coulomb effect, backwardscattering, loading, fogging, and etch.
 43. A stencil for chargedparticle beam lithography comprising: a first aperture comprising afirst diameter, wherein the first aperture is capable of forming, in oneshot, circular or nearly-circular patterns in a first range of sizes ona surface by varying shot dosage; and a second aperture comprising asecond diameter larger than the first diameter, wherein the secondaperture is capable of forming, in one shot, circular or nearly-circularpatterns in a second range of sizes on the surface by varying shotdosage, and wherein the first range of sizes is discontinuous with thesecond range of sizes.
 44. A system for forming patterns on a surfaceusing charged particle beam lithography comprising: a stencil comprisinga first aperture and a second aperture, wherein a first size of thefirst aperture is different than a second size of the second aperture; adevice configured to input a set of charged particle beam shots; and adevice configured to form circular or nearly circular patterns in afirst plurality of sizes using the first aperture and in a secondplurality of sizes using the second aperture.
 45. The system of claim 44wherein the first plurality of sizes overlaps the second plurality ofsizes.
 46. The system of claim 44 wherein the first plurality of sizesis discontinuous with the second plurality of sizes.
 47. The system ofclaim 44 wherein patterns can be formed in the first plurality of sizesusing the first aperture by varying dosage of shots in the set ofcharged particle beam shots.